A large vessel having a very small circular hole of diameter 1mm at the bottom is filled with water. Up to what maximum height (in cm ) water can be filled in the vessel so that there is no leakage? [surface tension of water =7.5× 10- 2 Nm- 1 and g=10ms- 2 ]

Question

A large vessel having a very small circular hole of diameter 1mm at the bottom is filled with water. Up to what maximum height (in cm ) water can be filled in the vessel so that there is no leakage? [surface tension of water =7.5× 10- 2 Nm- 1 and g=10ms- 2 ] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Water will not leak out from the hole if the weight of water in the water column is supported by the force due to surface tension.
Using the relation,

h = \frac{2 T}{r ρ g}

= \frac{2 \times 7.5 \times 1 0 ^{- 2}}{0.5 \times 1 0 ^{- 3} \times 1 0 ^{3} \times 10}

= 3 \times 1 0^{- 2} m = 3 c m

Q. A large vessel having a very small circular hole of diameter 1mm at the bottom is filled with water. Up to what maximum height (in cm ) water can be filled in the vessel so that there is no leakage? [surface tension of water =7.5×10−2Nm−1 and g=10ms−2 ]

Water will not leak out from the hole if the weight of water in the water column is supported by the force due to surface tension. Using the relation, h=rρg2T​ =0.5×10−3×103×102×7.5×10−2​ =3×10−2m=3cm

Q. A large vessel having a very small circular hole of diameter $1 mm$ at the bottom is filled with water. Up to what maximum height (in $c m$ ) water can be filled in the vessel so that there is no leakage? [surface tension of water $= 7.5 \times 1 0^{- 2} N m^{- 1}$ and $g = 10 m s^{- 2}$ ]

Water will not leak out from the hole if the weight of water in the water column is supported by the force due to surface tension.
Using the relation,
$h = \frac{2 T}{r ρ g}$
$= \frac{2 \times 7.5 \times 1 0 ^{- 2}}{0.5 \times 1 0 ^{- 3} \times 1 0 ^{3} \times 10}$
$= 3 \times 1 0^{- 2} m = 3 c m$